Transcript Permutations - Skyline R2 School

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Objective
Find the number of permutations of a set of
objects
Vocabulary
Permutation
An arrangement, or listing, of objects in which
order is important
Vocabulary
Factorial
The expression n! is the product of all counting
numbers beginning with n and counting backwards
to 1
4! = 4  3  2  1
24
Math Symbols
!
Factorial
Example 1 Evaluate Factorials
Example 2 Evaluate Factorials
Example 3 Find a Permutation
Example 4 Find a Permutation
Find the value of
Write problem
Write out definition of 4!
Multiply using
factorial key on
calculator
Answer: 24
1/4
Find the value of
Answer: 120
1/4
Find the value of the expression
Write problem
Write the definition of 3!
6  120
Answer:
Write the definition of 5!
Multiply using the
calculator
2/4
Find the value of the expression
Answer: 144
2/4
BOWLING A team of bowlers has five members who
bowl one at a time. In how many orders can they bowl?
5!
54321
Answer: 120 orders
This is an example of a permutation
Write the permutation
Write the definition of the
permutation
Multiply
3/4
TRACK AND FIELD A relay team has four members
who run one at a time. In how many orders can they
run?
Answer:
24 orders
3/4
RAFFLE A school fair holds a raffle with 1st, 2nd, and 3rd
prizes. Seven people enter the raffle. How many ways can
the three prizes be awarded?
7 choices for 6 choices for
1st prize
2nd prize
7
6
5 choices
formodified type of
This is a
3rd
prize
permutation
Since
5 the person with 1st
place cannot compete for 2nd
place, there only 6 people for
2nd prize
The people that won 1st and
2nd prizes cannot compete for
3rd prize
4/4
RAFFLE A school fair holds a raffle with 1st, 2nd, and 3rd
prizes. Seven people enter the raffle. How many ways can
the three prizes be awarded?
7 choices for 6 choices for
1st prize
2nd prize
7
6
765
5 choices for
3rd prize
5
Multiply the numbers
Answer: 210 ways
4/4
*
SAILING Nine boats are competing in a sailing race.
How many ways can medals for 1st, 2nd, and 3rd
place be awarded?
Answer:
504 ways
4/4
Assignment
Lesson 9:4
Permutations
3 - 19 All